6. Which statement is incorrect about clustered colomn charts?

The standard deviations are different within the sample datasets because it does not change with sample size but the standard error bars are smaller for the full data sets as there is more data to balance it out
The more datasets there are the less unreliable it is
When the error bars are confidence intervals, the rule of thumb is that two means differ significantly if each mean lies outside the confidence interval of the other one.
Clustered coloumn charts show four variables, length which changes continuously, country which has four categories, market which has two levels and also the mean of each
Each cluster show the the mean and the error bars

7. Which is not am R method of collecting a sample?

Reduction- making sure you use a precise representative sample size
Replication- need enough, gives us the power to achieve confidence in conclusions and ability to state mean with precision. Depends on the statistical error and variability in the sample data and also as many as possible given the time and resources.
Randomisation- this is where you avoid bias in order for estimates to be accurate. Each participant has an equal chance of being chosen

The application of probability levels to statements made about the sample and whether they fit with the true population parameters
Statistics from samples for population
Statistical methods used to make statements about the poplation
The process of moving from info about samples to statement about population

In order to incorporate both tails of the dataset
To work out the probability that we are at least 4 standard errors away from the sample mean, not that we are 4SE to the right of the sample mean.
to work out the probability that we are at least 4 standard errors away from the sample mean, not that we are 4SE to the left of the sample mean.

We can think of the difference between the two graphs as the amount of the overall variation that has been accounted for by using the country mean, instead of the overall mean.
The difference (1.32 – 1.08) is 0.24, and this is the variation we have accounted for. The remaining 1.08 is not explained by using the country mean instead of the overall mean: it is unexplained variance.
We have reduced the unexplained variance
There is more variation remaining to be accounted for (‘explained’) when the country mean is used than when the overall mean is used.
There is less variation remaining to be accounted for (‘explained’) when the country mean is used than when the overall mean is used.

The mean length of rice grains in the sample was 6.95 mm (95% CI: lower limit = 6.75 mm, upper limit = 7.15 mm, N = 100).
The mean was 6.75 mm at 95% CI and N=100
6.75 mm is less than mean length of rice grains in the sample is less than 7.15 mm (95% CI, N = 100).
Without this information we cannot sensibly interpret the statistic. Note that it is good practice to report the sample size, for similar reasons.
The mean length of rice grains in the sample was 6.95 ± 0.20 mm (95% CI, N = 100).
All sample statistics have confidence intervals and a statistic such as a sample mean is only meaningful when reported with its CI (or SD or SE, depending on context).

The critical value of t is completely different from the tabulated t value
The areas that lie outside the confidence interval lines are symmetrical and are known as the tabulated t-value which is also found in tables
Decide what level of confidence you want
Calculate your degrees of freedom by how many population parameters you have calculated

The chance of a Type II error rapidly increases. When we reduce alpha for each test, we lose power to find any real differences that exist
We need a test that compares lots of means at the same time, with one overall TI error rate of 5%, so have a good chance of detecting any real differences that exist. This is called analysis of variance- ANOVA and is based on the F test
Controls the TI rate
Controls the TII rate
We may well end up with no significant differences simply because we made it too difficult to find them. Type I and Type II errors trade off against each other.

Where you rank items that you measure depending on which has a more or less of an influence that we want to measure. Intervals are not necessarily equal and there is not true zero point
Where there are equal intervals between the data and an absolute zero, eg: time
Where you allocate a score to a category and it indicates a group of data
Where there are equal intervals of data on a continuous numerical scale, eg: farenheit

F test compares variances by variance 1 + variance 2
The F test needs to range from infinity because sometime the explained variance can be smaller than the unexplained variance
F test compares variances by variance 1 - variance 2
ANOVA classes variance 1 as the variance accounted for (model) and variance 2 is the error variance (not accounted for)

When the variances, sample size and mean of the two samples are equal, the df reduction is more
If both the variances and the sample sizes are different, df ranges from a little less than Na+Nb–2 when the bigger sample has the bigger variance to a lot less when the smaller sample has the bigger variance.
The main thing to remember about the d.f. in the unequal-variances t-test is that it can be fractional.
The formula is used to allow for the fact that the variances (and often the sample sizes) are not equal. The adjustment produces what we can call ‘effective’ or ‘adjusted’ degrees of freedom. T distribution can take fractional d.f values
If the variances are different and the sample sizes are the same, df is less than Na+Nb–2, the reduction being more when the difference in variance is bigger.
The formula for d.f. in the unequal-variances two-sample t-test is quite complex
If the variances are the same and the sample sizes are different, df is less than Na+Nb–2, the reduction being more the more the difference in sample size.